I want to know if I can travel with my passport within the US being in immigration process?
I will be okay using only my passport ?
For travel in the US (which I did in April) you only need your passport as a form of ID. This is for the immigration process (you'll need a visa, most likely, in your passport), and for all internal flights as well.
It is possible to fly internally without a passport as a foreigner, as an English friend did in April as well, but it was VERY difficult, as every security person expects you to have your passport available to travel with.